1,1,106,112,1.735135,"\text{Not used}","int((a + b/sin(c + d*x)^2)^4,x)","a^4\,x-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(\frac{3\,b^4}{5}+\frac{4\,a\,b^3}{5}\right)+{\mathrm{tan}\left(c+d\,x\right)}^6\,\left(4\,a^3\,b+6\,a^2\,b^2+4\,a\,b^3+b^4\right)+{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(2\,a^2\,b^2+\frac{8\,a\,b^3}{3}+b^4\right)+\frac{b^4}{7}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^7}","Not used",1,"a^4*x - (tan(c + d*x)^2*((4*a*b^3)/5 + (3*b^4)/5) + tan(c + d*x)^6*(4*a*b^3 + 4*a^3*b + b^4 + 6*a^2*b^2) + tan(c + d*x)^4*((8*a*b^3)/3 + b^4 + 2*a^2*b^2) + b^4/7)/(d*tan(c + d*x)^7)","B"
2,1,70,74,0.426702,"\text{Not used}","int((a + b/sin(c + d*x)^2)^3,x)","a^3\,x-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(\frac{2\,b^3}{3}+a\,b^2\right)+{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(3\,a^2\,b+3\,a\,b^2+b^3\right)+\frac{b^3}{5}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^5}","Not used",1,"a^3*x - (tan(c + d*x)^2*(a*b^2 + (2*b^3)/3) + tan(c + d*x)^4*(3*a*b^2 + 3*a^2*b + b^3) + b^3/5)/(d*tan(c + d*x)^5)","B"
3,1,42,41,0.148713,"\text{Not used}","int((a + b/sin(c + d*x)^2)^2,x)","a^2\,x-\frac{{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(b^2+2\,a\,b\right)+\frac{b^2}{3}}{d\,{\mathrm{tan}\left(c+d\,x\right)}^3}","Not used",1,"a^2*x - (tan(c + d*x)^2*(2*a*b + b^2) + b^2/3)/(d*tan(c + d*x)^3)","B"
4,1,16,16,0.101443,"\text{Not used}","int(a + b/sin(c + d*x)^2,x)","a\,x-\frac{b\,\mathrm{cot}\left(c+d\,x\right)}{d}","Not used",1,"a*x - (b*cot(c + d*x))/d","B"
5,1,104,46,0.250891,"\text{Not used}","int(1/(a + b/sin(c + d*x)^2),x)","\frac{\mathrm{atan}\left(\frac{2\,a\,b^2\,\mathrm{tan}\left(c+d\,x\right)}{2\,a^2\,b+2\,a\,b^2}+\frac{2\,a^2\,b\,\mathrm{tan}\left(c+d\,x\right)}{2\,a^2\,b+2\,a\,b^2}\right)}{a\,d}+\frac{\mathrm{atanh}\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,\left(a+b\right)}}{b}\right)\,\sqrt{-b\,\left(a+b\right)}}{d\,\left(a^2+b\,a\right)}","Not used",1,"atan((2*a*b^2*tan(c + d*x))/(2*a*b^2 + 2*a^2*b) + (2*a^2*b*tan(c + d*x))/(2*a*b^2 + 2*a^2*b))/(a*d) + (atanh((tan(c + d*x)*(-b*(a + b))^(1/2))/b)*(-b*(a + b))^(1/2))/(d*(a*b + a^2))","B"
6,1,1958,92,1.988872,"\text{Not used}","int(1/(a + b/sin(c + d*x)^2)^2,x)","\frac{b\,\mathrm{tan}\left(c+d\,x\right)}{2\,a\,d\,\left(\left(a+b\right)\,{\mathrm{tan}\left(c+d\,x\right)}^2+b\right)\,\left(a+b\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^8+80\,a^7\,b+144\,a^6\,b^2+112\,a^5\,b^3+32\,a^4\,b^4\right)}{8\,a^2\,\left(a^3+b\,a^2\right)}+\frac{\left(2\,a^6\,b+4\,a^5\,b^2+2\,a^4\,b^3\right)\,1{}\mathrm{i}}{2\,\left(a^4+b\,a^3\right)}}{2\,a^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4+16\,a^3\,b+33\,a^2\,b^2+28\,a\,b^3+8\,b^4\right)}{4\,\left(a^3+b\,a^2\right)}}{a^2}-\frac{\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^8+80\,a^7\,b+144\,a^6\,b^2+112\,a^5\,b^3+32\,a^4\,b^4\right)}{8\,a^2\,\left(a^3+b\,a^2\right)}+\frac{\left(2\,a^6\,b+4\,a^5\,b^2+2\,a^4\,b^3\right)\,1{}\mathrm{i}}{2\,\left(a^4+b\,a^3\right)}}{2\,a^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4+16\,a^3\,b+33\,a^2\,b^2+28\,a\,b^3+8\,b^4\right)}{4\,\left(a^3+b\,a^2\right)}}{a^2}}{\frac{3\,a^2\,b+\frac{7\,a\,b^2}{2}+b^3}{a^4+b\,a^3}+\frac{\frac{\left(-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^8+80\,a^7\,b+144\,a^6\,b^2+112\,a^5\,b^3+32\,a^4\,b^4\right)}{8\,a^2\,\left(a^3+b\,a^2\right)}+\frac{\left(2\,a^6\,b+4\,a^5\,b^2+2\,a^4\,b^3\right)\,1{}\mathrm{i}}{2\,\left(a^4+b\,a^3\right)}\right)\,1{}\mathrm{i}}{2\,a^2}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4+16\,a^3\,b+33\,a^2\,b^2+28\,a\,b^3+8\,b^4\right)\,1{}\mathrm{i}}{4\,\left(a^3+b\,a^2\right)}}{a^2}+\frac{\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(16\,a^8+80\,a^7\,b+144\,a^6\,b^2+112\,a^5\,b^3+32\,a^4\,b^4\right)}{8\,a^2\,\left(a^3+b\,a^2\right)}+\frac{\left(2\,a^6\,b+4\,a^5\,b^2+2\,a^4\,b^3\right)\,1{}\mathrm{i}}{2\,\left(a^4+b\,a^3\right)}\right)\,1{}\mathrm{i}}{2\,a^2}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4+16\,a^3\,b+33\,a^2\,b^2+28\,a\,b^3+8\,b^4\right)\,1{}\mathrm{i}}{4\,\left(a^3+b\,a^2\right)}}{a^2}}\right)}{a^2\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4+16\,a^3\,b+33\,a^2\,b^2+28\,a\,b^3+8\,b^4\right)}{2\,\left(a^3+b\,a^2\right)}-\frac{\left(\frac{2\,a^6\,b+4\,a^5\,b^2+2\,a^4\,b^3}{a^4+b\,a^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,\left(16\,a^8+80\,a^7\,b+144\,a^6\,b^2+112\,a^5\,b^3+32\,a^4\,b^4\right)}{8\,\left(a^3+b\,a^2\right)\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\left(3\,a+2\,b\right)\,1{}\mathrm{i}}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}+\frac{\sqrt{-b\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4+16\,a^3\,b+33\,a^2\,b^2+28\,a\,b^3+8\,b^4\right)}{2\,\left(a^3+b\,a^2\right)}+\frac{\left(\frac{2\,a^6\,b+4\,a^5\,b^2+2\,a^4\,b^3}{a^4+b\,a^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,\left(16\,a^8+80\,a^7\,b+144\,a^6\,b^2+112\,a^5\,b^3+32\,a^4\,b^4\right)}{8\,\left(a^3+b\,a^2\right)\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\left(3\,a+2\,b\right)\,1{}\mathrm{i}}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}}{\frac{3\,a^2\,b+\frac{7\,a\,b^2}{2}+b^3}{a^4+b\,a^3}-\frac{\sqrt{-b\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4+16\,a^3\,b+33\,a^2\,b^2+28\,a\,b^3+8\,b^4\right)}{2\,\left(a^3+b\,a^2\right)}-\frac{\left(\frac{2\,a^6\,b+4\,a^5\,b^2+2\,a^4\,b^3}{a^4+b\,a^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,\left(16\,a^8+80\,a^7\,b+144\,a^6\,b^2+112\,a^5\,b^3+32\,a^4\,b^4\right)}{8\,\left(a^3+b\,a^2\right)\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}+\frac{\sqrt{-b\,{\left(a+b\right)}^3}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(4\,a^4+16\,a^3\,b+33\,a^2\,b^2+28\,a\,b^3+8\,b^4\right)}{2\,\left(a^3+b\,a^2\right)}+\frac{\left(\frac{2\,a^6\,b+4\,a^5\,b^2+2\,a^4\,b^3}{a^4+b\,a^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,\left(16\,a^8+80\,a^7\,b+144\,a^6\,b^2+112\,a^5\,b^3+32\,a^4\,b^4\right)}{8\,\left(a^3+b\,a^2\right)\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}\right)\,\left(3\,a+2\,b\right)}{4\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}}\right)\,\sqrt{-b\,{\left(a+b\right)}^3}\,\left(3\,a+2\,b\right)\,1{}\mathrm{i}}{2\,d\,\left(a^5+3\,a^4\,b+3\,a^3\,b^2+a^2\,b^3\right)}","Not used",1,"(b*tan(c + d*x))/(2*a*d*(b + tan(c + d*x)^2*(a + b))*(a + b)) - (atan((((-b*(a + b)^3)^(1/2)*((tan(c + d*x)*(28*a*b^3 + 16*a^3*b + 4*a^4 + 8*b^4 + 33*a^2*b^2))/(2*(a^2*b + a^3)) - (((2*a^6*b + 2*a^4*b^3 + 4*a^5*b^2)/(a^3*b + a^4) - (tan(c + d*x)*(-b*(a + b)^3)^(1/2)*(3*a + 2*b)*(80*a^7*b + 16*a^8 + 32*a^4*b^4 + 112*a^5*b^3 + 144*a^6*b^2))/(8*(a^2*b + a^3)*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(-b*(a + b)^3)^(1/2)*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(3*a + 2*b)*1i)/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) + ((-b*(a + b)^3)^(1/2)*((tan(c + d*x)*(28*a*b^3 + 16*a^3*b + 4*a^4 + 8*b^4 + 33*a^2*b^2))/(2*(a^2*b + a^3)) + (((2*a^6*b + 2*a^4*b^3 + 4*a^5*b^2)/(a^3*b + a^4) + (tan(c + d*x)*(-b*(a + b)^3)^(1/2)*(3*a + 2*b)*(80*a^7*b + 16*a^8 + 32*a^4*b^4 + 112*a^5*b^3 + 144*a^6*b^2))/(8*(a^2*b + a^3)*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(-b*(a + b)^3)^(1/2)*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(3*a + 2*b)*1i)/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))/(((7*a*b^2)/2 + 3*a^2*b + b^3)/(a^3*b + a^4) - ((-b*(a + b)^3)^(1/2)*((tan(c + d*x)*(28*a*b^3 + 16*a^3*b + 4*a^4 + 8*b^4 + 33*a^2*b^2))/(2*(a^2*b + a^3)) - (((2*a^6*b + 2*a^4*b^3 + 4*a^5*b^2)/(a^3*b + a^4) - (tan(c + d*x)*(-b*(a + b)^3)^(1/2)*(3*a + 2*b)*(80*a^7*b + 16*a^8 + 32*a^4*b^4 + 112*a^5*b^3 + 144*a^6*b^2))/(8*(a^2*b + a^3)*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(-b*(a + b)^3)^(1/2)*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) + ((-b*(a + b)^3)^(1/2)*((tan(c + d*x)*(28*a*b^3 + 16*a^3*b + 4*a^4 + 8*b^4 + 33*a^2*b^2))/(2*(a^2*b + a^3)) + (((2*a^6*b + 2*a^4*b^3 + 4*a^5*b^2)/(a^3*b + a^4) + (tan(c + d*x)*(-b*(a + b)^3)^(1/2)*(3*a + 2*b)*(80*a^7*b + 16*a^8 + 32*a^4*b^4 + 112*a^5*b^3 + 144*a^6*b^2))/(8*(a^2*b + a^3)*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(-b*(a + b)^3)^(1/2)*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)))*(3*a + 2*b))/(4*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2))))*(-b*(a + b)^3)^(1/2)*(3*a + 2*b)*1i)/(2*d*(3*a^4*b + a^5 + a^2*b^3 + 3*a^3*b^2)) - atan((((((2*a^6*b + 2*a^4*b^3 + 4*a^5*b^2)*1i)/(2*(a^3*b + a^4)) - (tan(c + d*x)*(80*a^7*b + 16*a^8 + 32*a^4*b^4 + 112*a^5*b^3 + 144*a^6*b^2))/(8*a^2*(a^2*b + a^3)))/(2*a^2) + (tan(c + d*x)*(28*a*b^3 + 16*a^3*b + 4*a^4 + 8*b^4 + 33*a^2*b^2))/(4*(a^2*b + a^3)))/a^2 - ((((2*a^6*b + 2*a^4*b^3 + 4*a^5*b^2)*1i)/(2*(a^3*b + a^4)) + (tan(c + d*x)*(80*a^7*b + 16*a^8 + 32*a^4*b^4 + 112*a^5*b^3 + 144*a^6*b^2))/(8*a^2*(a^2*b + a^3)))/(2*a^2) - (tan(c + d*x)*(28*a*b^3 + 16*a^3*b + 4*a^4 + 8*b^4 + 33*a^2*b^2))/(4*(a^2*b + a^3)))/a^2)/(((7*a*b^2)/2 + 3*a^2*b + b^3)/(a^3*b + a^4) + (((((2*a^6*b + 2*a^4*b^3 + 4*a^5*b^2)*1i)/(2*(a^3*b + a^4)) - (tan(c + d*x)*(80*a^7*b + 16*a^8 + 32*a^4*b^4 + 112*a^5*b^3 + 144*a^6*b^2))/(8*a^2*(a^2*b + a^3)))*1i)/(2*a^2) + (tan(c + d*x)*(28*a*b^3 + 16*a^3*b + 4*a^4 + 8*b^4 + 33*a^2*b^2)*1i)/(4*(a^2*b + a^3)))/a^2 + (((((2*a^6*b + 2*a^4*b^3 + 4*a^5*b^2)*1i)/(2*(a^3*b + a^4)) + (tan(c + d*x)*(80*a^7*b + 16*a^8 + 32*a^4*b^4 + 112*a^5*b^3 + 144*a^6*b^2))/(8*a^2*(a^2*b + a^3)))*1i)/(2*a^2) - (tan(c + d*x)*(28*a*b^3 + 16*a^3*b + 4*a^4 + 8*b^4 + 33*a^2*b^2)*1i)/(4*(a^2*b + a^3)))/a^2))/(a^2*d)","B"
7,1,3189,144,3.926117,"\text{Not used}","int(1/(a + b/sin(c + d*x)^2)^3,x)","\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(4\,b^2+9\,a\,b\right)}{8\,\left(a^3+b\,a^2\right)}+\frac{b\,\mathrm{tan}\left(c+d\,x\right)\,\left(4\,b^2+7\,a\,b\right)}{8\,\left(a^4+2\,a^3\,b+a^2\,b^2\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^4\,\left(a^2+2\,a\,b+b^2\right)+b^2+{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(2\,b^2+2\,a\,b\right)\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^{12}+1792\,a^{11}\,b+5120\,a^{10}\,b^2+7680\,a^9\,b^3+6400\,a^8\,b^4+2816\,a^7\,b^5+512\,a^6\,b^6\right)}{128\,a^3\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}+\frac{\left(\frac{7\,a^{10}\,b}{2}+\frac{25\,a^9\,b^2}{2}+\frac{33\,a^8\,b^3}{2}+\frac{19\,a^7\,b^4}{2}+2\,a^6\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3\right)}}{2\,a^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^6+384\,a^5\,b+1185\,a^4\,b^2+1880\,a^3\,b^3+1600\,a^2\,b^4+704\,a\,b^5+128\,b^6\right)}{64\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}}{a^3}-\frac{\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^{12}+1792\,a^{11}\,b+5120\,a^{10}\,b^2+7680\,a^9\,b^3+6400\,a^8\,b^4+2816\,a^7\,b^5+512\,a^6\,b^6\right)}{128\,a^3\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}+\frac{\left(\frac{7\,a^{10}\,b}{2}+\frac{25\,a^9\,b^2}{2}+\frac{33\,a^8\,b^3}{2}+\frac{19\,a^7\,b^4}{2}+2\,a^6\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3\right)}}{2\,a^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^6+384\,a^5\,b+1185\,a^4\,b^2+1880\,a^3\,b^3+1600\,a^2\,b^4+704\,a\,b^5+128\,b^6\right)}{64\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}}{a^3}}{\frac{\frac{15\,a^4\,b}{4}+\frac{295\,a^3\,b^2}{32}+\frac{19\,a^2\,b^3}{2}+\frac{19\,a\,b^4}{4}+b^5}{a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3}+\frac{\frac{\left(-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^{12}+1792\,a^{11}\,b+5120\,a^{10}\,b^2+7680\,a^9\,b^3+6400\,a^8\,b^4+2816\,a^7\,b^5+512\,a^6\,b^6\right)}{128\,a^3\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}+\frac{\left(\frac{7\,a^{10}\,b}{2}+\frac{25\,a^9\,b^2}{2}+\frac{33\,a^8\,b^3}{2}+\frac{19\,a^7\,b^4}{2}+2\,a^6\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3\right)}\right)\,1{}\mathrm{i}}{2\,a^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^6+384\,a^5\,b+1185\,a^4\,b^2+1880\,a^3\,b^3+1600\,a^2\,b^4+704\,a\,b^5+128\,b^6\right)\,1{}\mathrm{i}}{64\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}}{a^3}+\frac{\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^{12}+1792\,a^{11}\,b+5120\,a^{10}\,b^2+7680\,a^9\,b^3+6400\,a^8\,b^4+2816\,a^7\,b^5+512\,a^6\,b^6\right)}{128\,a^3\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}+\frac{\left(\frac{7\,a^{10}\,b}{2}+\frac{25\,a^9\,b^2}{2}+\frac{33\,a^8\,b^3}{2}+\frac{19\,a^7\,b^4}{2}+2\,a^6\,b^5\right)\,1{}\mathrm{i}}{2\,\left(a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3\right)}\right)\,1{}\mathrm{i}}{2\,a^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^6+384\,a^5\,b+1185\,a^4\,b^2+1880\,a^3\,b^3+1600\,a^2\,b^4+704\,a\,b^5+128\,b^6\right)\,1{}\mathrm{i}}{64\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}}{a^3}}\right)}{a^3\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\sqrt{-b\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^6+384\,a^5\,b+1185\,a^4\,b^2+1880\,a^3\,b^3+1600\,a^2\,b^4+704\,a\,b^5+128\,b^6\right)}{32\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}-\frac{\sqrt{-b\,{\left(a+b\right)}^5}\,\left(\frac{\frac{7\,a^{10}\,b}{2}+\frac{25\,a^9\,b^2}{2}+\frac{33\,a^8\,b^3}{2}+\frac{19\,a^7\,b^4}{2}+2\,a^6\,b^5}{a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^5}\,\left(15\,a^2+20\,a\,b+8\,b^2\right)\,\left(256\,a^{12}+1792\,a^{11}\,b+5120\,a^{10}\,b^2+7680\,a^9\,b^3+6400\,a^8\,b^4+2816\,a^7\,b^5+512\,a^6\,b^6\right)}{512\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}\right)\,\left(15\,a^2+20\,a\,b+8\,b^2\right)}{16\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}\right)\,\left(15\,a^2+20\,a\,b+8\,b^2\right)\,1{}\mathrm{i}}{16\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}+\frac{\sqrt{-b\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^6+384\,a^5\,b+1185\,a^4\,b^2+1880\,a^3\,b^3+1600\,a^2\,b^4+704\,a\,b^5+128\,b^6\right)}{32\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}+\frac{\sqrt{-b\,{\left(a+b\right)}^5}\,\left(\frac{\frac{7\,a^{10}\,b}{2}+\frac{25\,a^9\,b^2}{2}+\frac{33\,a^8\,b^3}{2}+\frac{19\,a^7\,b^4}{2}+2\,a^6\,b^5}{a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^5}\,\left(15\,a^2+20\,a\,b+8\,b^2\right)\,\left(256\,a^{12}+1792\,a^{11}\,b+5120\,a^{10}\,b^2+7680\,a^9\,b^3+6400\,a^8\,b^4+2816\,a^7\,b^5+512\,a^6\,b^6\right)}{512\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}\right)\,\left(15\,a^2+20\,a\,b+8\,b^2\right)}{16\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}\right)\,\left(15\,a^2+20\,a\,b+8\,b^2\right)\,1{}\mathrm{i}}{16\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}}{\frac{\frac{15\,a^4\,b}{4}+\frac{295\,a^3\,b^2}{32}+\frac{19\,a^2\,b^3}{2}+\frac{19\,a\,b^4}{4}+b^5}{a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3}-\frac{\sqrt{-b\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^6+384\,a^5\,b+1185\,a^4\,b^2+1880\,a^3\,b^3+1600\,a^2\,b^4+704\,a\,b^5+128\,b^6\right)}{32\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}-\frac{\sqrt{-b\,{\left(a+b\right)}^5}\,\left(\frac{\frac{7\,a^{10}\,b}{2}+\frac{25\,a^9\,b^2}{2}+\frac{33\,a^8\,b^3}{2}+\frac{19\,a^7\,b^4}{2}+2\,a^6\,b^5}{a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^5}\,\left(15\,a^2+20\,a\,b+8\,b^2\right)\,\left(256\,a^{12}+1792\,a^{11}\,b+5120\,a^{10}\,b^2+7680\,a^9\,b^3+6400\,a^8\,b^4+2816\,a^7\,b^5+512\,a^6\,b^6\right)}{512\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}\right)\,\left(15\,a^2+20\,a\,b+8\,b^2\right)}{16\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}\right)\,\left(15\,a^2+20\,a\,b+8\,b^2\right)}{16\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}+\frac{\sqrt{-b\,{\left(a+b\right)}^5}\,\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(64\,a^6+384\,a^5\,b+1185\,a^4\,b^2+1880\,a^3\,b^3+1600\,a^2\,b^4+704\,a\,b^5+128\,b^6\right)}{32\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)}+\frac{\sqrt{-b\,{\left(a+b\right)}^5}\,\left(\frac{\frac{7\,a^{10}\,b}{2}+\frac{25\,a^9\,b^2}{2}+\frac{33\,a^8\,b^3}{2}+\frac{19\,a^7\,b^4}{2}+2\,a^6\,b^5}{a^9+3\,a^8\,b+3\,a^7\,b^2+a^6\,b^3}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^5}\,\left(15\,a^2+20\,a\,b+8\,b^2\right)\,\left(256\,a^{12}+1792\,a^{11}\,b+5120\,a^{10}\,b^2+7680\,a^9\,b^3+6400\,a^8\,b^4+2816\,a^7\,b^5+512\,a^6\,b^6\right)}{512\,\left(a^7+3\,a^6\,b+3\,a^5\,b^2+a^4\,b^3\right)\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}\right)\,\left(15\,a^2+20\,a\,b+8\,b^2\right)}{16\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}\right)\,\left(15\,a^2+20\,a\,b+8\,b^2\right)}{16\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}}\right)\,\sqrt{-b\,{\left(a+b\right)}^5}\,\left(15\,a^2+20\,a\,b+8\,b^2\right)\,1{}\mathrm{i}}{8\,d\,\left(a^8+5\,a^7\,b+10\,a^6\,b^2+10\,a^5\,b^3+5\,a^4\,b^4+a^3\,b^5\right)}","Not used",1,"((tan(c + d*x)^3*(9*a*b + 4*b^2))/(8*(a^2*b + a^3)) + (b*tan(c + d*x)*(7*a*b + 4*b^2))/(8*(2*a^3*b + a^4 + a^2*b^2)))/(d*(tan(c + d*x)^4*(2*a*b + a^2 + b^2) + b^2 + tan(c + d*x)^2*(2*a*b + 2*b^2))) - atan(((((((7*a^10*b)/2 + 2*a^6*b^5 + (19*a^7*b^4)/2 + (33*a^8*b^3)/2 + (25*a^9*b^2)/2)*1i)/(2*(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2)) - (tan(c + d*x)*(1792*a^11*b + 256*a^12 + 512*a^6*b^6 + 2816*a^7*b^5 + 6400*a^8*b^4 + 7680*a^9*b^3 + 5120*a^10*b^2))/(128*a^3*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)))/(2*a^3) + (tan(c + d*x)*(704*a*b^5 + 384*a^5*b + 64*a^6 + 128*b^6 + 1600*a^2*b^4 + 1880*a^3*b^3 + 1185*a^4*b^2))/(64*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)))/a^3 - (((((7*a^10*b)/2 + 2*a^6*b^5 + (19*a^7*b^4)/2 + (33*a^8*b^3)/2 + (25*a^9*b^2)/2)*1i)/(2*(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2)) + (tan(c + d*x)*(1792*a^11*b + 256*a^12 + 512*a^6*b^6 + 2816*a^7*b^5 + 6400*a^8*b^4 + 7680*a^9*b^3 + 5120*a^10*b^2))/(128*a^3*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)))/(2*a^3) - (tan(c + d*x)*(704*a*b^5 + 384*a^5*b + 64*a^6 + 128*b^6 + 1600*a^2*b^4 + 1880*a^3*b^3 + 1185*a^4*b^2))/(64*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)))/a^3)/(((19*a*b^4)/4 + (15*a^4*b)/4 + b^5 + (19*a^2*b^3)/2 + (295*a^3*b^2)/32)/(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2) + ((((((7*a^10*b)/2 + 2*a^6*b^5 + (19*a^7*b^4)/2 + (33*a^8*b^3)/2 + (25*a^9*b^2)/2)*1i)/(2*(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2)) - (tan(c + d*x)*(1792*a^11*b + 256*a^12 + 512*a^6*b^6 + 2816*a^7*b^5 + 6400*a^8*b^4 + 7680*a^9*b^3 + 5120*a^10*b^2))/(128*a^3*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)))*1i)/(2*a^3) + (tan(c + d*x)*(704*a*b^5 + 384*a^5*b + 64*a^6 + 128*b^6 + 1600*a^2*b^4 + 1880*a^3*b^3 + 1185*a^4*b^2)*1i)/(64*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)))/a^3 + ((((((7*a^10*b)/2 + 2*a^6*b^5 + (19*a^7*b^4)/2 + (33*a^8*b^3)/2 + (25*a^9*b^2)/2)*1i)/(2*(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2)) + (tan(c + d*x)*(1792*a^11*b + 256*a^12 + 512*a^6*b^6 + 2816*a^7*b^5 + 6400*a^8*b^4 + 7680*a^9*b^3 + 5120*a^10*b^2))/(128*a^3*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)))*1i)/(2*a^3) - (tan(c + d*x)*(704*a*b^5 + 384*a^5*b + 64*a^6 + 128*b^6 + 1600*a^2*b^4 + 1880*a^3*b^3 + 1185*a^4*b^2)*1i)/(64*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)))/a^3))/(a^3*d) - (atan((((-b*(a + b)^5)^(1/2)*((tan(c + d*x)*(704*a*b^5 + 384*a^5*b + 64*a^6 + 128*b^6 + 1600*a^2*b^4 + 1880*a^3*b^3 + 1185*a^4*b^2))/(32*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)) - ((-b*(a + b)^5)^(1/2)*(((7*a^10*b)/2 + 2*a^6*b^5 + (19*a^7*b^4)/2 + (33*a^8*b^3)/2 + (25*a^9*b^2)/2)/(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2) - (tan(c + d*x)*(-b*(a + b)^5)^(1/2)*(20*a*b + 15*a^2 + 8*b^2)*(1792*a^11*b + 256*a^12 + 512*a^6*b^6 + 2816*a^7*b^5 + 6400*a^8*b^4 + 7680*a^9*b^3 + 5120*a^10*b^2))/(512*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))*(20*a*b + 15*a^2 + 8*b^2))/(16*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))*(20*a*b + 15*a^2 + 8*b^2)*1i)/(16*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)) + ((-b*(a + b)^5)^(1/2)*((tan(c + d*x)*(704*a*b^5 + 384*a^5*b + 64*a^6 + 128*b^6 + 1600*a^2*b^4 + 1880*a^3*b^3 + 1185*a^4*b^2))/(32*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)) + ((-b*(a + b)^5)^(1/2)*(((7*a^10*b)/2 + 2*a^6*b^5 + (19*a^7*b^4)/2 + (33*a^8*b^3)/2 + (25*a^9*b^2)/2)/(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2) + (tan(c + d*x)*(-b*(a + b)^5)^(1/2)*(20*a*b + 15*a^2 + 8*b^2)*(1792*a^11*b + 256*a^12 + 512*a^6*b^6 + 2816*a^7*b^5 + 6400*a^8*b^4 + 7680*a^9*b^3 + 5120*a^10*b^2))/(512*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))*(20*a*b + 15*a^2 + 8*b^2))/(16*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))*(20*a*b + 15*a^2 + 8*b^2)*1i)/(16*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))/(((19*a*b^4)/4 + (15*a^4*b)/4 + b^5 + (19*a^2*b^3)/2 + (295*a^3*b^2)/32)/(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2) - ((-b*(a + b)^5)^(1/2)*((tan(c + d*x)*(704*a*b^5 + 384*a^5*b + 64*a^6 + 128*b^6 + 1600*a^2*b^4 + 1880*a^3*b^3 + 1185*a^4*b^2))/(32*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)) - ((-b*(a + b)^5)^(1/2)*(((7*a^10*b)/2 + 2*a^6*b^5 + (19*a^7*b^4)/2 + (33*a^8*b^3)/2 + (25*a^9*b^2)/2)/(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2) - (tan(c + d*x)*(-b*(a + b)^5)^(1/2)*(20*a*b + 15*a^2 + 8*b^2)*(1792*a^11*b + 256*a^12 + 512*a^6*b^6 + 2816*a^7*b^5 + 6400*a^8*b^4 + 7680*a^9*b^3 + 5120*a^10*b^2))/(512*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))*(20*a*b + 15*a^2 + 8*b^2))/(16*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))*(20*a*b + 15*a^2 + 8*b^2))/(16*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)) + ((-b*(a + b)^5)^(1/2)*((tan(c + d*x)*(704*a*b^5 + 384*a^5*b + 64*a^6 + 128*b^6 + 1600*a^2*b^4 + 1880*a^3*b^3 + 1185*a^4*b^2))/(32*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)) + ((-b*(a + b)^5)^(1/2)*(((7*a^10*b)/2 + 2*a^6*b^5 + (19*a^7*b^4)/2 + (33*a^8*b^3)/2 + (25*a^9*b^2)/2)/(3*a^8*b + a^9 + a^6*b^3 + 3*a^7*b^2) + (tan(c + d*x)*(-b*(a + b)^5)^(1/2)*(20*a*b + 15*a^2 + 8*b^2)*(1792*a^11*b + 256*a^12 + 512*a^6*b^6 + 2816*a^7*b^5 + 6400*a^8*b^4 + 7680*a^9*b^3 + 5120*a^10*b^2))/(512*(3*a^6*b + a^7 + a^4*b^3 + 3*a^5*b^2)*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))*(20*a*b + 15*a^2 + 8*b^2))/(16*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2)))*(20*a*b + 15*a^2 + 8*b^2))/(16*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2))))*(-b*(a + b)^5)^(1/2)*(20*a*b + 15*a^2 + 8*b^2)*1i)/(8*d*(5*a^7*b + a^8 + a^3*b^5 + 5*a^4*b^4 + 10*a^5*b^3 + 10*a^6*b^2))","B"
8,1,4447,204,4.764477,"\text{Not used}","int(1/(a + b/sin(c + d*x)^2)^4,x)","\frac{\frac{{\mathrm{tan}\left(c+d\,x\right)}^5\,\left(29\,a^2\,b+26\,a\,b^2+8\,b^3\right)}{16\,\left(a^4+b\,a^3\right)}+\frac{{\mathrm{tan}\left(c+d\,x\right)}^3\,\left(17\,a^2\,b^2+18\,a\,b^3+6\,b^4\right)}{6\,\left(a^5+2\,a^4\,b+a^3\,b^2\right)}+\frac{b^2\,\mathrm{tan}\left(c+d\,x\right)\,\left(19\,a^2\,b+22\,a\,b^2+8\,b^3\right)}{16\,\left(a^6+3\,a^5\,b+3\,a^4\,b^2+a^3\,b^3\right)}}{d\,\left({\mathrm{tan}\left(c+d\,x\right)}^6\,\left(a^3+3\,a^2\,b+3\,a\,b^2+b^3\right)+{\mathrm{tan}\left(c+d\,x\right)}^2\,\left(3\,b^3+3\,a\,b^2\right)+{\mathrm{tan}\left(c+d\,x\right)}^4\,\left(3\,a^2\,b+6\,a\,b^2+3\,b^3\right)+b^3\right)}-\frac{\mathrm{atan}\left(\frac{\frac{\frac{-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^{16}+9216\,a^{15}\,b+35840\,a^{14}\,b^2+78848\,a^{13}\,b^3+107520\,a^{12}\,b^4+93184\,a^{11}\,b^5+50176\,a^{10}\,b^6+15360\,a^9\,b^7+2048\,a^8\,b^8\right)}{512\,a^4\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}+\frac{\left(\frac{19\,a^{14}\,b}{4}+\frac{49\,a^{13}\,b^2}{2}+\frac{105\,a^{12}\,b^3}{2}+60\,a^{11}\,b^4+\frac{155\,a^{10}\,b^5}{4}+\frac{27\,a^9\,b^6}{2}+2\,a^8\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5\right)}}{2\,a^4}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^8+2048\,a^7\,b+8393\,a^6\,b^2+19236\,a^5\,b^3+26740\,a^4\,b^4+23296\,a^3\,b^5+12544\,a^2\,b^6+3840\,a\,b^7+512\,b^8\right)}{256\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}}{a^4}-\frac{\frac{\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^{16}+9216\,a^{15}\,b+35840\,a^{14}\,b^2+78848\,a^{13}\,b^3+107520\,a^{12}\,b^4+93184\,a^{11}\,b^5+50176\,a^{10}\,b^6+15360\,a^9\,b^7+2048\,a^8\,b^8\right)}{512\,a^4\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}+\frac{\left(\frac{19\,a^{14}\,b}{4}+\frac{49\,a^{13}\,b^2}{2}+\frac{105\,a^{12}\,b^3}{2}+60\,a^{11}\,b^4+\frac{155\,a^{10}\,b^5}{4}+\frac{27\,a^9\,b^6}{2}+2\,a^8\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5\right)}}{2\,a^4}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^8+2048\,a^7\,b+8393\,a^6\,b^2+19236\,a^5\,b^3+26740\,a^4\,b^4+23296\,a^3\,b^5+12544\,a^2\,b^6+3840\,a\,b^7+512\,b^8\right)}{256\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}}{a^4}}{\frac{\frac{35\,a^6\,b}{8}+\frac{2135\,a^5\,b^2}{128}+\frac{959\,a^4\,b^3}{32}+\frac{995\,a^3\,b^4}{32}+\frac{155\,a^2\,b^5}{8}+\frac{27\,a\,b^6}{4}+b^7}{a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5}+\frac{\frac{\left(-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^{16}+9216\,a^{15}\,b+35840\,a^{14}\,b^2+78848\,a^{13}\,b^3+107520\,a^{12}\,b^4+93184\,a^{11}\,b^5+50176\,a^{10}\,b^6+15360\,a^9\,b^7+2048\,a^8\,b^8\right)}{512\,a^4\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}+\frac{\left(\frac{19\,a^{14}\,b}{4}+\frac{49\,a^{13}\,b^2}{2}+\frac{105\,a^{12}\,b^3}{2}+60\,a^{11}\,b^4+\frac{155\,a^{10}\,b^5}{4}+\frac{27\,a^9\,b^6}{2}+2\,a^8\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5\right)}\right)\,1{}\mathrm{i}}{2\,a^4}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^8+2048\,a^7\,b+8393\,a^6\,b^2+19236\,a^5\,b^3+26740\,a^4\,b^4+23296\,a^3\,b^5+12544\,a^2\,b^6+3840\,a\,b^7+512\,b^8\right)\,1{}\mathrm{i}}{256\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}}{a^4}+\frac{\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(1024\,a^{16}+9216\,a^{15}\,b+35840\,a^{14}\,b^2+78848\,a^{13}\,b^3+107520\,a^{12}\,b^4+93184\,a^{11}\,b^5+50176\,a^{10}\,b^6+15360\,a^9\,b^7+2048\,a^8\,b^8\right)}{512\,a^4\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}+\frac{\left(\frac{19\,a^{14}\,b}{4}+\frac{49\,a^{13}\,b^2}{2}+\frac{105\,a^{12}\,b^3}{2}+60\,a^{11}\,b^4+\frac{155\,a^{10}\,b^5}{4}+\frac{27\,a^9\,b^6}{2}+2\,a^8\,b^7\right)\,1{}\mathrm{i}}{2\,\left(a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5\right)}\right)\,1{}\mathrm{i}}{2\,a^4}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^8+2048\,a^7\,b+8393\,a^6\,b^2+19236\,a^5\,b^3+26740\,a^4\,b^4+23296\,a^3\,b^5+12544\,a^2\,b^6+3840\,a\,b^7+512\,b^8\right)\,1{}\mathrm{i}}{256\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}}{a^4}}\right)}{a^4\,d}-\frac{\mathrm{atan}\left(\frac{\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^8+2048\,a^7\,b+8393\,a^6\,b^2+19236\,a^5\,b^3+26740\,a^4\,b^4+23296\,a^3\,b^5+12544\,a^2\,b^6+3840\,a\,b^7+512\,b^8\right)}{128\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}-\frac{\sqrt{-b\,{\left(a+b\right)}^7}\,\left(\frac{\frac{19\,a^{14}\,b}{4}+\frac{49\,a^{13}\,b^2}{2}+\frac{105\,a^{12}\,b^3}{2}+60\,a^{11}\,b^4+\frac{155\,a^{10}\,b^5}{4}+\frac{27\,a^9\,b^6}{2}+2\,a^8\,b^7}{a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)\,\left(1024\,a^{16}+9216\,a^{15}\,b+35840\,a^{14}\,b^2+78848\,a^{13}\,b^3+107520\,a^{12}\,b^4+93184\,a^{11}\,b^5+50176\,a^{10}\,b^6+15360\,a^9\,b^7+2048\,a^8\,b^8\right)}{4096\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}\right)\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)}{32\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)\,1{}\mathrm{i}}{32\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}+\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^8+2048\,a^7\,b+8393\,a^6\,b^2+19236\,a^5\,b^3+26740\,a^4\,b^4+23296\,a^3\,b^5+12544\,a^2\,b^6+3840\,a\,b^7+512\,b^8\right)}{128\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}+\frac{\sqrt{-b\,{\left(a+b\right)}^7}\,\left(\frac{\frac{19\,a^{14}\,b}{4}+\frac{49\,a^{13}\,b^2}{2}+\frac{105\,a^{12}\,b^3}{2}+60\,a^{11}\,b^4+\frac{155\,a^{10}\,b^5}{4}+\frac{27\,a^9\,b^6}{2}+2\,a^8\,b^7}{a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)\,\left(1024\,a^{16}+9216\,a^{15}\,b+35840\,a^{14}\,b^2+78848\,a^{13}\,b^3+107520\,a^{12}\,b^4+93184\,a^{11}\,b^5+50176\,a^{10}\,b^6+15360\,a^9\,b^7+2048\,a^8\,b^8\right)}{4096\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}\right)\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)}{32\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)\,1{}\mathrm{i}}{32\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}}{\frac{\frac{35\,a^6\,b}{8}+\frac{2135\,a^5\,b^2}{128}+\frac{959\,a^4\,b^3}{32}+\frac{995\,a^3\,b^4}{32}+\frac{155\,a^2\,b^5}{8}+\frac{27\,a\,b^6}{4}+b^7}{a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5}-\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^8+2048\,a^7\,b+8393\,a^6\,b^2+19236\,a^5\,b^3+26740\,a^4\,b^4+23296\,a^3\,b^5+12544\,a^2\,b^6+3840\,a\,b^7+512\,b^8\right)}{128\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}-\frac{\sqrt{-b\,{\left(a+b\right)}^7}\,\left(\frac{\frac{19\,a^{14}\,b}{4}+\frac{49\,a^{13}\,b^2}{2}+\frac{105\,a^{12}\,b^3}{2}+60\,a^{11}\,b^4+\frac{155\,a^{10}\,b^5}{4}+\frac{27\,a^9\,b^6}{2}+2\,a^8\,b^7}{a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5}-\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)\,\left(1024\,a^{16}+9216\,a^{15}\,b+35840\,a^{14}\,b^2+78848\,a^{13}\,b^3+107520\,a^{12}\,b^4+93184\,a^{11}\,b^5+50176\,a^{10}\,b^6+15360\,a^9\,b^7+2048\,a^8\,b^8\right)}{4096\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}\right)\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)}{32\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)}{32\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}+\frac{\left(\frac{\mathrm{tan}\left(c+d\,x\right)\,\left(256\,a^8+2048\,a^7\,b+8393\,a^6\,b^2+19236\,a^5\,b^3+26740\,a^4\,b^4+23296\,a^3\,b^5+12544\,a^2\,b^6+3840\,a\,b^7+512\,b^8\right)}{128\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)}+\frac{\sqrt{-b\,{\left(a+b\right)}^7}\,\left(\frac{\frac{19\,a^{14}\,b}{4}+\frac{49\,a^{13}\,b^2}{2}+\frac{105\,a^{12}\,b^3}{2}+60\,a^{11}\,b^4+\frac{155\,a^{10}\,b^5}{4}+\frac{27\,a^9\,b^6}{2}+2\,a^8\,b^7}{a^{14}+5\,a^{13}\,b+10\,a^{12}\,b^2+10\,a^{11}\,b^3+5\,a^{10}\,b^4+a^9\,b^5}+\frac{\mathrm{tan}\left(c+d\,x\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)\,\left(1024\,a^{16}+9216\,a^{15}\,b+35840\,a^{14}\,b^2+78848\,a^{13}\,b^3+107520\,a^{12}\,b^4+93184\,a^{11}\,b^5+50176\,a^{10}\,b^6+15360\,a^9\,b^7+2048\,a^8\,b^8\right)}{4096\,\left(a^{11}+5\,a^{10}\,b+10\,a^9\,b^2+10\,a^8\,b^3+5\,a^7\,b^4+a^6\,b^5\right)\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}\right)\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)}{32\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)}{32\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}}\right)\,\sqrt{-b\,{\left(a+b\right)}^7}\,\left(35\,a^3+70\,a^2\,b+56\,a\,b^2+16\,b^3\right)\,1{}\mathrm{i}}{16\,d\,\left(a^{11}+7\,a^{10}\,b+21\,a^9\,b^2+35\,a^8\,b^3+35\,a^7\,b^4+21\,a^6\,b^5+7\,a^5\,b^6+a^4\,b^7\right)}","Not used",1,"((tan(c + d*x)^5*(26*a*b^2 + 29*a^2*b + 8*b^3))/(16*(a^3*b + a^4)) + (tan(c + d*x)^3*(18*a*b^3 + 6*b^4 + 17*a^2*b^2))/(6*(2*a^4*b + a^5 + a^3*b^2)) + (b^2*tan(c + d*x)*(22*a*b^2 + 19*a^2*b + 8*b^3))/(16*(3*a^5*b + a^6 + a^3*b^3 + 3*a^4*b^2)))/(d*(tan(c + d*x)^6*(3*a*b^2 + 3*a^2*b + a^3 + b^3) + tan(c + d*x)^2*(3*a*b^2 + 3*b^3) + tan(c + d*x)^4*(6*a*b^2 + 3*a^2*b + 3*b^3) + b^3)) - atan(((((((19*a^14*b)/4 + 2*a^8*b^7 + (27*a^9*b^6)/2 + (155*a^10*b^5)/4 + 60*a^11*b^4 + (105*a^12*b^3)/2 + (49*a^13*b^2)/2)*1i)/(2*(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2)) - (tan(c + d*x)*(9216*a^15*b + 1024*a^16 + 2048*a^8*b^8 + 15360*a^9*b^7 + 50176*a^10*b^6 + 93184*a^11*b^5 + 107520*a^12*b^4 + 78848*a^13*b^3 + 35840*a^14*b^2))/(512*a^4*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)))/(2*a^4) + (tan(c + d*x)*(3840*a*b^7 + 2048*a^7*b + 256*a^8 + 512*b^8 + 12544*a^2*b^6 + 23296*a^3*b^5 + 26740*a^4*b^4 + 19236*a^5*b^3 + 8393*a^6*b^2))/(256*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)))/a^4 - (((((19*a^14*b)/4 + 2*a^8*b^7 + (27*a^9*b^6)/2 + (155*a^10*b^5)/4 + 60*a^11*b^4 + (105*a^12*b^3)/2 + (49*a^13*b^2)/2)*1i)/(2*(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2)) + (tan(c + d*x)*(9216*a^15*b + 1024*a^16 + 2048*a^8*b^8 + 15360*a^9*b^7 + 50176*a^10*b^6 + 93184*a^11*b^5 + 107520*a^12*b^4 + 78848*a^13*b^3 + 35840*a^14*b^2))/(512*a^4*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)))/(2*a^4) - (tan(c + d*x)*(3840*a*b^7 + 2048*a^7*b + 256*a^8 + 512*b^8 + 12544*a^2*b^6 + 23296*a^3*b^5 + 26740*a^4*b^4 + 19236*a^5*b^3 + 8393*a^6*b^2))/(256*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)))/a^4)/(((27*a*b^6)/4 + (35*a^6*b)/8 + b^7 + (155*a^2*b^5)/8 + (995*a^3*b^4)/32 + (959*a^4*b^3)/32 + (2135*a^5*b^2)/128)/(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2) + ((((((19*a^14*b)/4 + 2*a^8*b^7 + (27*a^9*b^6)/2 + (155*a^10*b^5)/4 + 60*a^11*b^4 + (105*a^12*b^3)/2 + (49*a^13*b^2)/2)*1i)/(2*(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2)) - (tan(c + d*x)*(9216*a^15*b + 1024*a^16 + 2048*a^8*b^8 + 15360*a^9*b^7 + 50176*a^10*b^6 + 93184*a^11*b^5 + 107520*a^12*b^4 + 78848*a^13*b^3 + 35840*a^14*b^2))/(512*a^4*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)))*1i)/(2*a^4) + (tan(c + d*x)*(3840*a*b^7 + 2048*a^7*b + 256*a^8 + 512*b^8 + 12544*a^2*b^6 + 23296*a^3*b^5 + 26740*a^4*b^4 + 19236*a^5*b^3 + 8393*a^6*b^2)*1i)/(256*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)))/a^4 + ((((((19*a^14*b)/4 + 2*a^8*b^7 + (27*a^9*b^6)/2 + (155*a^10*b^5)/4 + 60*a^11*b^4 + (105*a^12*b^3)/2 + (49*a^13*b^2)/2)*1i)/(2*(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2)) + (tan(c + d*x)*(9216*a^15*b + 1024*a^16 + 2048*a^8*b^8 + 15360*a^9*b^7 + 50176*a^10*b^6 + 93184*a^11*b^5 + 107520*a^12*b^4 + 78848*a^13*b^3 + 35840*a^14*b^2))/(512*a^4*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)))*1i)/(2*a^4) - (tan(c + d*x)*(3840*a*b^7 + 2048*a^7*b + 256*a^8 + 512*b^8 + 12544*a^2*b^6 + 23296*a^3*b^5 + 26740*a^4*b^4 + 19236*a^5*b^3 + 8393*a^6*b^2)*1i)/(256*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)))/a^4))/(a^4*d) - (atan(((((tan(c + d*x)*(3840*a*b^7 + 2048*a^7*b + 256*a^8 + 512*b^8 + 12544*a^2*b^6 + 23296*a^3*b^5 + 26740*a^4*b^4 + 19236*a^5*b^3 + 8393*a^6*b^2))/(128*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)) - ((-b*(a + b)^7)^(1/2)*(((19*a^14*b)/4 + 2*a^8*b^7 + (27*a^9*b^6)/2 + (155*a^10*b^5)/4 + 60*a^11*b^4 + (105*a^12*b^3)/2 + (49*a^13*b^2)/2)/(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2) - (tan(c + d*x)*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3)*(9216*a^15*b + 1024*a^16 + 2048*a^8*b^8 + 15360*a^9*b^7 + 50176*a^10*b^6 + 93184*a^11*b^5 + 107520*a^12*b^4 + 78848*a^13*b^3 + 35840*a^14*b^2))/(4096*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3))/(32*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3)*1i)/(32*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)) + (((tan(c + d*x)*(3840*a*b^7 + 2048*a^7*b + 256*a^8 + 512*b^8 + 12544*a^2*b^6 + 23296*a^3*b^5 + 26740*a^4*b^4 + 19236*a^5*b^3 + 8393*a^6*b^2))/(128*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)) + ((-b*(a + b)^7)^(1/2)*(((19*a^14*b)/4 + 2*a^8*b^7 + (27*a^9*b^6)/2 + (155*a^10*b^5)/4 + 60*a^11*b^4 + (105*a^12*b^3)/2 + (49*a^13*b^2)/2)/(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2) + (tan(c + d*x)*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3)*(9216*a^15*b + 1024*a^16 + 2048*a^8*b^8 + 15360*a^9*b^7 + 50176*a^10*b^6 + 93184*a^11*b^5 + 107520*a^12*b^4 + 78848*a^13*b^3 + 35840*a^14*b^2))/(4096*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3))/(32*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3)*1i)/(32*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))/(((27*a*b^6)/4 + (35*a^6*b)/8 + b^7 + (155*a^2*b^5)/8 + (995*a^3*b^4)/32 + (959*a^4*b^3)/32 + (2135*a^5*b^2)/128)/(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2) - (((tan(c + d*x)*(3840*a*b^7 + 2048*a^7*b + 256*a^8 + 512*b^8 + 12544*a^2*b^6 + 23296*a^3*b^5 + 26740*a^4*b^4 + 19236*a^5*b^3 + 8393*a^6*b^2))/(128*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)) - ((-b*(a + b)^7)^(1/2)*(((19*a^14*b)/4 + 2*a^8*b^7 + (27*a^9*b^6)/2 + (155*a^10*b^5)/4 + 60*a^11*b^4 + (105*a^12*b^3)/2 + (49*a^13*b^2)/2)/(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2) - (tan(c + d*x)*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3)*(9216*a^15*b + 1024*a^16 + 2048*a^8*b^8 + 15360*a^9*b^7 + 50176*a^10*b^6 + 93184*a^11*b^5 + 107520*a^12*b^4 + 78848*a^13*b^3 + 35840*a^14*b^2))/(4096*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3))/(32*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3))/(32*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)) + (((tan(c + d*x)*(3840*a*b^7 + 2048*a^7*b + 256*a^8 + 512*b^8 + 12544*a^2*b^6 + 23296*a^3*b^5 + 26740*a^4*b^4 + 19236*a^5*b^3 + 8393*a^6*b^2))/(128*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)) + ((-b*(a + b)^7)^(1/2)*(((19*a^14*b)/4 + 2*a^8*b^7 + (27*a^9*b^6)/2 + (155*a^10*b^5)/4 + 60*a^11*b^4 + (105*a^12*b^3)/2 + (49*a^13*b^2)/2)/(5*a^13*b + a^14 + a^9*b^5 + 5*a^10*b^4 + 10*a^11*b^3 + 10*a^12*b^2) + (tan(c + d*x)*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3)*(9216*a^15*b + 1024*a^16 + 2048*a^8*b^8 + 15360*a^9*b^7 + 50176*a^10*b^6 + 93184*a^11*b^5 + 107520*a^12*b^4 + 78848*a^13*b^3 + 35840*a^14*b^2))/(4096*(5*a^10*b + a^11 + a^6*b^5 + 5*a^7*b^4 + 10*a^8*b^3 + 10*a^9*b^2)*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3))/(32*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2)))*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3))/(32*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2))))*(-b*(a + b)^7)^(1/2)*(56*a*b^2 + 70*a^2*b + 35*a^3 + 16*b^3)*1i)/(16*d*(7*a^10*b + a^11 + a^4*b^7 + 7*a^5*b^6 + 21*a^6*b^5 + 35*a^7*b^4 + 35*a^8*b^3 + 21*a^9*b^2))","B"
9,0,-1,167,0.000000,"\text{Not used}","int((a + b/sin(c + d*x)^2)^(5/2),x)","\int {\left(a+\frac{b}{{\sin\left(c+d\,x\right)}^2}\right)}^{5/2} \,d x","Not used",1,"int((a + b/sin(c + d*x)^2)^(5/2), x)","F"
10,0,-1,119,0.000000,"\text{Not used}","int((a + b/sin(c + d*x)^2)^(3/2),x)","\int {\left(a+\frac{b}{{\sin\left(c+d\,x\right)}^2}\right)}^{3/2} \,d x","Not used",1,"int((a + b/sin(c + d*x)^2)^(3/2), x)","F"
11,0,-1,81,0.000000,"\text{Not used}","int((a + b/sin(c + d*x)^2)^(1/2),x)","\int \sqrt{a+\frac{b}{{\sin\left(c+d\,x\right)}^2}} \,d x","Not used",1,"int((a + b/sin(c + d*x)^2)^(1/2), x)","F"
12,0,-1,39,0.000000,"\text{Not used}","int(1/(a + b/sin(c + d*x)^2)^(1/2),x)","\int \frac{1}{\sqrt{a+\frac{b}{{\sin\left(c+d\,x\right)}^2}}} \,d x","Not used",1,"int(1/(a + b/sin(c + d*x)^2)^(1/2), x)","F"
13,0,-1,77,0.000000,"\text{Not used}","int(1/(a + b/sin(c + d*x)^2)^(3/2),x)","\int \frac{1}{{\left(a+\frac{b}{{\sin\left(c+d\,x\right)}^2}\right)}^{3/2}} \,d x","Not used",1,"int(1/(a + b/sin(c + d*x)^2)^(3/2), x)","F"
14,0,-1,126,0.000000,"\text{Not used}","int(1/(a + b/sin(c + d*x)^2)^(5/2),x)","\int \frac{1}{{\left(a+\frac{b}{{\sin\left(c+d\,x\right)}^2}\right)}^{5/2}} \,d x","Not used",1,"int(1/(a + b/sin(c + d*x)^2)^(5/2), x)","F"
15,0,-1,180,0.000000,"\text{Not used}","int(1/(a + b/sin(c + d*x)^2)^(7/2),x)","\int \frac{1}{{\left(a+\frac{b}{{\sin\left(c+d\,x\right)}^2}\right)}^{7/2}} \,d x","Not used",1,"int(1/(a + b/sin(c + d*x)^2)^(7/2), x)","F"
16,0,-1,44,0.000000,"\text{Not used}","int((1/sin(x)^2 + 1)^(3/2),x)","\int {\left(\frac{1}{{\sin\left(x\right)}^2}+1\right)}^{3/2} \,d x","Not used",1,"int((1/sin(x)^2 + 1)^(3/2), x)","F"
17,0,-1,28,0.000000,"\text{Not used}","int((1/sin(x)^2 + 1)^(1/2),x)","\int \sqrt{\frac{1}{{\sin\left(x\right)}^2}+1} \,d x","Not used",1,"int((1/sin(x)^2 + 1)^(1/2), x)","F"
18,0,-1,16,0.000000,"\text{Not used}","int(1/(1/sin(x)^2 + 1)^(1/2),x)","\int \frac{1}{\sqrt{\frac{1}{{\sin\left(x\right)}^2}+1}} \,d x","Not used",1,"int(1/(1/sin(x)^2 + 1)^(1/2), x)","F"
19,0,-1,33,0.000000,"\text{Not used}","int((1 - 1/sin(x)^2)^(3/2),x)","\int {\left(1-\frac{1}{{\sin\left(x\right)}^2}\right)}^{3/2} \,d x","Not used",1,"int((1 - 1/sin(x)^2)^(3/2), x)","F"
20,0,-1,16,0.000000,"\text{Not used}","int((1 - 1/sin(x)^2)^(1/2),x)","\int \sqrt{1-\frac{1}{{\sin\left(x\right)}^2}} \,d x","Not used",1,"int((1 - 1/sin(x)^2)^(1/2), x)","F"
21,0,-1,17,0.000000,"\text{Not used}","int(1/(1 - 1/sin(x)^2)^(1/2),x)","\int \frac{1}{\sqrt{1-\frac{1}{{\sin\left(x\right)}^2}}} \,d x","Not used",1,"int(1/(1 - 1/sin(x)^2)^(1/2), x)","F"
22,0,-1,30,0.000000,"\text{Not used}","int((1/sin(x)^2 - 1)^(3/2),x)","\int {\left(\frac{1}{{\sin\left(x\right)}^2}-1\right)}^{3/2} \,d x","Not used",1,"int((1/sin(x)^2 - 1)^(3/2), x)","F"
23,0,-1,14,0.000000,"\text{Not used}","int((1/sin(x)^2 - 1)^(1/2),x)","\int \sqrt{\frac{1}{{\sin\left(x\right)}^2}-1} \,d x","Not used",1,"int((1/sin(x)^2 - 1)^(1/2), x)","F"
24,0,-1,15,0.000000,"\text{Not used}","int(1/(1/sin(x)^2 - 1)^(1/2),x)","\int \frac{1}{\sqrt{\frac{1}{{\sin\left(x\right)}^2}-1}} \,d x","Not used",1,"int(1/(1/sin(x)^2 - 1)^(1/2), x)","F"
25,0,-1,55,0.000000,"\text{Not used}","int((- 1/sin(x)^2 - 1)^(3/2),x)","\int {\left(-\frac{1}{{\sin\left(x\right)}^2}-1\right)}^{3/2} \,d x","Not used",1,"int((- 1/sin(x)^2 - 1)^(3/2), x)","F"
26,0,-1,33,0.000000,"\text{Not used}","int((- 1/sin(x)^2 - 1)^(1/2),x)","\int \sqrt{-\frac{1}{{\sin\left(x\right)}^2}-1} \,d x","Not used",1,"int((- 1/sin(x)^2 - 1)^(1/2), x)","F"
27,0,-1,18,0.000000,"\text{Not used}","int(1/(- 1/sin(x)^2 - 1)^(1/2),x)","\int \frac{1}{\sqrt{-\frac{1}{{\sin\left(x\right)}^2}-1}} \,d x","Not used",1,"int(1/(- 1/sin(x)^2 - 1)^(1/2), x)","F"